DISPLAY OF FRICTION IN VIRTUAL ENVIRONMENTS BASED ON HUMAN FINGER
PAD CHARACTERISTICS
A. Nahvi, J.M. Hollerbach, R. Freier, D.D. Nelson
Depts. Mechanical Engineering and Computer Science
Univ. Utah, Salt Lake City, UT 84112
ABSTRACT
A friction display system is proposed for virtual environments. Since a user’s fingertip is often placed inside a ring or
thimble of a haptic interface , the finger pad cannot move relative to the finger structure as freely as it would move in the real
world. Thus, it is necessary to imitate the real world movement
of the human finger pad in the virtual environment. This paper
quantifies the frictional properties of the human finger pad on 9
subjects by simultaneously recording force and movement of the
finger pad when it rubs against a rigid plate. Results of such tests
and implementation in a virtual environment are reported.
INTRODUCTION
Designers of complex mechanical assemblies typically create physical prototypes to evaluate part interaction, ease of assembly, and functionality. To avoid this time-consuming and
costly procedure, virtual prototyping seeks instead to employ realistic simulation and immersive interfaces. Although mechanical CAD systems provide realistic visual displays, they do not
permit a designer to manipulate and interact with mechanical elements in a realistic manner. For example, a haptic interface coupled with a visual display would allow a designer to evaluate car
dashboard designs [22] and to experience assembly forces [7].
In the real world, we rub on the surfaces of objects to sense
their roughness, texture, discontinuity of curvature, etc. Similarly, imposing tangential forces on the users of haptic display
systems creates a significant sense of realness in virtual environment. Without imposing friction in the virtual world, all objects
are perceived as slippery as an icy surface.
Recently, there have been a number of research works to
display friction in the virtual environment. Chen et al. [1] developed a 2-D spring model by using the concept of contact area
to unify the forces due to friction and adhesion. Salcudean and
Vlaar [16] presented a stick-slip model, which employs a velocity threshold to define sticking, but which only employs a viscous
friction during slipping. A stick-slip friction model which uses
Coulomb friction in the slip phase was employed by Salisbury et
al. [17]. However, these works have not included human finger
pad frictional characteristics in their friction models. Unlike in
the real world, in many haptic interfaces, a fingertip is placed inside a ring or thimble. Thus, the finger pad cannot be displaced
relative to the thimble to create the same sense of touch as in the
real world. For this reason, a haptic interface must artificially
create the displacements and forces as would be created by a real
frictional surface. This paper is the first attempt in integrating
finger pad characteristics with the virtual friction model.
Although there have been a number of recent works on the
normal properties of the finger pad [6, 15, 18, 20, 21], frictional
properties of the finger pad have not been explored much. Han
et al. [8] investigated human fingers to mimic in making robot
fingers. They found that the finger pad coefficient of friction
increases significantly for small normal forces (e.g. 2N), and
is relatively constant for bigger normal forces. In the field of
teleoperation, Edin et al. [2] investigated the effect of slippage
on relaying friction to the master operator.
In the next section, a simplified basic stick-slip friction
model is explained first. Then finger pad frictional characteristics are explored and incorporated in the basic model. Display
of friction in virtual environments using this model is also illustrated.
BASIC STICK-SLIP MODEL
Assume the haptic interface is moving against a surface. In
the slip phase, the friction force f f is:
ff
µd
n
v
v
if
v
vmin
(1)
y
path
(i) Solid: y (slip); dotted: y (stick); dashed: stick center
a
vmin
0.1
k || n||
0.05
y (m)
f
c
a
c
0
−0.05
−0.1
0
x
0.4
v (m/s)
0.2
z
Figure 1. TRANSITION FROM
PLIFIED MODEL.
SLIP to STICK PHASE
0.5
1
1.5
2
2.5
(ii) Solid: v (slip); dotted: v (stick); dashed: +/− v_min
a
0
−0.2
IN THE SIM-
−0.4
0
0.5
1
1.5
2
(iii) Solid: f_f (slip); dotted: f_f (stick)
2.5
0.5
2.5
5
where µd is the dynamic coefficient of friction, n is the magnitude of normal force, v is the tangential velocity of the haptic
interface, and vmin is a small threshold velocity. As soon as v
becomes smaller than vmin , the stick phase begins.
It is more intuitive to explain the stick phase in a simplified
form first. Later, the incorporation of pulp frictional behavior
into this simplified model will be explained.
Figure 1 shows the transition from slip to stick phase. Point
a represents the transition point where the velocity reaches a
threshold of vmin . During this transition, a virtual spring is
formed whose stiffness k f n is proportional to the normal
force. It pulls the haptic interface towards c (stick center). The
spring force at this moment is:
ff
kf
n
a c
µd
n
v
v
(2)
As long
as the spring force is less than the static friction limit
µs n , the stick phase holds. In other words,
the haptic interface
is trapped in a circle of radius µs µd a-c centered at c. c is
found by:
c
µd
a
kf
n
n
v
v
a
µd
kf
v
v
(3)
where v is the velocity just before transition. It can be easily shown that the maximum stick radius is µ s k f . The harder
the contact materials of surface and haptic interface, the bigger
k f . The slip phase
begins
when the haptic interface is µ s k f or
equally µs µd a c away from c. We can imagine that the
virtual spring has a rupture limit of µs n .
Figure 2 shows a one-dimensional simulation of position,
velocity, and friction force of a haptic interface moving tangentially against a wall. It is assumed that normal force is constant
a
f_f (N)
0
−5
0
1
1.5
2
Time (s)
Figure 2. SIMULATION OF STICK-SLIP FRICTION FORCE IN THE BASIC MODEL.
and there is a sinusoidal tangential motion. It shows that when
velocity becomes as slow as vmin , the stick phase (dotted) begins.
The dashed line in Figure 2(i) shows stick center position. A
slight increase in y after the onset of the stick phase at point a,
causes a slight increase in virtual spring force f f. Then
y de
creases until the force in the virtual spring
is
µ
n
.
At
this
s
point, friction suddenly changes to µd n of the slip phase.
Note that the change of force is continuous in transition from the
slip to the stick phase, and discontinuous in transition from the
stick to the slip phase.
FINGERTIP FRICTIONAL CHARACTERISTICS
In order to have a realistic model of the stick-slip friction, we
need to incorporate the frictional properties of the pulp into our
model. Skin is thick, glabrous, and rich in sweat glands. Nerve
endings are found in abundance in the skin [4]. Soft subcutaneous adipose tissue forms an almost continuous layer beneath
skin. Blood vessels and lymphatics form a rich network throughout the adipose tissue. This tissue can be distorted readily and it
slowly resumes its original shape [12]. An abundance of nerves
also run through this tissue.
Stick Ellipse
The stick region of the pulp should be evaluated. 9 subjects
were asked to press on a paper-coated, flat, and rigid plate with
−3
4
Camera
α
Wires
3.5
Force
sensor
z
x
y
3
Normalized a (m)
LEDs
x 10
Rigid plate
2.5
2
1.5
Figure 3. THE EXPERIMENTAL SETUP FOR MEASURING FINGER
PAD FRICTIONAL CHARACTERISTICS.
−5
1
Fitted line: a = −3.7 x 10
−3
alpha + 4.4 x 10
0.5
0.846
0
0
10
20
30
40
0.845
α (deg)
50
60
70
80
90
Figure 5. MAJOR AXIS OF THE NORMALIZED STICK ELLIPSE (IN
LATERAL DIRECTION) VERSUS THE FINGER ANGLE.
0.844
z (m)
0.843
0.842
−3
4
0.841
0.84
x 10
3.5
0.839
3
−0.094
−0.092
−0.09
y (m)
−0.088
−0.086
−0.084
Figure 4. THE STICK ELLIPSE OF THE PULP. SOLID: EXPERIMENTAL DATA; DASHED: FITTED ELLIPSE.
Normalized b (m)
0.838
−0.096
2.5
2
1.5
their index finger and exert both normal and tangential forces as
far as no slip occurred. Subjects were between 23 and 51 years
old (mean = 32.5, standard deviation = 7.8). 8 were males and 1
was female. 3 had relatively callous finger pads and 6 had relatively soft finger pads. As shown in Figure 3, the fingertip position and inclination angle of the finger relative to the plate were
determined by two IRED markers attached on top of proximal
and distal segments of the finger. Three-dimensional locations
of IREDs were determined by an optoelectronic tracking device
called Optotrak 3020 (Northern Digital, Ltd., Waterloo, Ontario,
Canada) which has a stated accuracy of 0.1 - 0.15 mm in a 2.5
m distance. The contact force was measured by a six-axis force
and torque sensor JR3 model 67M25 (JR3, Inc., Woodland, California) which was placed under the flat plate. Position and force
signals were recorded synchronously.
Figure 4 shows a typical result of this experiment where a
subject tried to move along the largest possible curve in the yz
plane, while the center of his fingertip remained almost fixed.
It shows an ellipse rather than a circle. Figures 5 and 6 show
the normalized axes of this ellipse for all subjects. It shows that
both major and minor axes shorten as finger angle with contact
plane α increases. All subjects showed a similar linear trend
1
Fitted line: b = −2.0 x 10−5 alpha + 3.3 x 10−3
0.5
0
0
10
20
30
40
α (deg)
50
60
70
80
90
Figure 6. MINOR AXIS OF THE NORMALIZED STICK ELLIPSE (IN
LONGITUDINAL DIRECTION) VERSUS THE FINGER ANGLE.
of decreasing axes versus α. However, the length of axes were
different for each subject. The value of axes at α 45 deg was
used to normalize axes lengths for all subjects. Two lines were
fitted for axes a and b as displayed in Figures 5 and 6. Since
it was not possible to collect equal number of samples for all
subjects, the least squares error vector was multiplied by a weight
matrix so that all subjects have equal role in the final fitted lines
[13]. Figure 7 combines Figures 5 and 6 into a single figure and
shows the stick ellipse for different angles of finger.
Therefore, we must deviate from our basic stick-slip model
in two ways:
1. We need to have a stick ellipse rather than a circle.
−0.4
z (m)
100
−0.6
−0.8
0
60
vz (m/s)
0
−0.2
−0.4
−0.6
0
20
0.2
40
20
0.8
1
a
a
a
1.2
0.2
0.4
0.6
0.8
1
1.2
0.2
0.4
0.6
0.8
1
1.2
10
0
−3
x 10
0.6
fx (N)
0
5
0.4
−5
z (m)
−4
4
2
0
−2
−3
x 10
y (m)
Figure 7. THE NORMALIZED STICK ELLIPSE FOR DIFFERENT FINGER ANGLES.
10 Normal force fx (N): mean = 23.4, std. dev. = 3.3, min. = 14.3, max. = 31.3
0
0
1.5
1
0.5
0
−0.5
0
a
a
a
µ
α (deg)
80
0.2
0.4
0.6
0.8
Time (s)
1
1.2
ffy (N)
5
Figure 9.
0
−5
−10
−0.436
−0.434
−0.432
−0.43
Fingertip y position (m)
−0.428
−0.426
10 Normal force fx (N): mean = 24.8, std. dev. = 3.3, min. = 19.9, max. = 33.1
fz
f (N)
5
0
−5
−10
−0.604
−0.603
−0.602
−0.601
−0.6
−0.599
−0.598
Fingertip z position (m)
−0.597
−0.596
−0.595
Figure 8. THE LINEAR RELATIONSHIP BETWEEN FRICTION FORCE
AND FINGER PAD DISPLACEMENT.
2. Stick ellipse gets smaller as α increases.
Force-Displacement Relationship in Stick Phase
The relationship between the tangential force and displacement of the pulp should be obtained. 11 subjects were asked
to push back and forth along two perpendicular directions sequentially along lateral (y) and longitudinal (z) directions without slippage. The angle between finger and plate remained fixed
at a convenient angle, e.g. 45 deg. Figure 8 shows the typical
results for one subject. It shows a linear relationship between
friction and displacement. Therefore, we can keep our earlier
assumption of a linear spring as outlined in Section 2.
CHANGE OF PHASE FROM SLIP TO STICK.
Switching from Slip Phase to Stick Phase
In Section 2, it was stated that when velocity becomes
smaller than a threshold vmin , slip phase ends and stick phase
begins. We need to determine vmin based on behavior of the human finger pad. 11 subjects were asked to frequently slip and
stick on the plate along a tangential axis z as shown in Figure 9
for one subject. In the figure, velocity vz , normal force f x , and
µ f f z fx are also shown. Points a show the end of slip phase
which is accompanied by a distinct change in µ. It is seen that
phase change occurs at an absolute velocity of vmin 0 1m s.
High Frequency Oscillation in Slip Phase
When we rub on a dry surface, a high-frequency vibration is
produced as we move on the surface. This has to be incorporated
into the slip phase model. The lack of such an oscillation in
virtual environments creates a feeling of moving in a fluid rather
than rubbing on a dry surface. An experiment was performed to
obtain the vibrational behavior of the pulp in the slip phase. A
subject was asked to move his fingers tangentially on a flat plate
in the z direction, while pressing gently on it in the normal x
direction. Figure 10 show the results for position and force of
the fingertip in x and z directions. The oscillation of position and
force signals are evident in those figures. The sampling rate for
both position and force was 1000 Hz. Figure 11 shows the power
spectrum density for tangential and normal forces. The peak of
vibration is at 89 Hz for this test. Stochastic models [3, 5, 19] are
appropriate to create such an oscillation in virtual environments.
Howe and Cutkosky [10] have also reported experimental results
1
0.18
0.16
0.14
1.22
1.24
1.26
0
1.28
−0.5
0
2.013
2
4
6
8
10
12
2
4
6
8
10
12
2
4
6
Time (s)
8
10
12
20
2.0125
10
f
2.012
f (N)
x (m)
0.5
y (m)
z (m)
0.2
1.22
1.24
1.26
1.28
−10
20
f_z (N)
0
10
−20
0
0
0.4
0.2
−10
1.24
1.26
1.28
µ
1.22
f_x (N)
10
−0.2
5
−0.4
0
0
−5
1.22
1.24
1.26
1.28
Time (s)
Figure 10. x and
AND FORCE.
z
COMPONENTS OF THE FINGERTIP POSITION
PSD of f_z
300
200
Peak at 89 Hz
100
0
0
200
PSD for f_x
0
100
200
300
400
500
Figure 12. FRICTION ON A VIRTUAL PLANE IN THE y DIRECTION.
POSITION, FRICTION FORCE, AND COEFFICIENT OF FRICTION ARE
SHOWN.
Arm Master, an advanced hydraulic force-reflecting exoskeleton
[11, 9, 23]. Figure 12 shows the preliminary experimental results of friction in a tangential y direction on a flat plane with
coefficients of friction µs 0 3 and µd 0 2. The data were
recorded at 500 Hz. Regions of relatively constant coefficient
of friction represent slip phase and the transient regions represent stick phase. The users reported a feeling of moving a rubber
eraser against a paper.
Peak at 89 Hz
150
100
50
0
0
100
200
300
Frequency (Hz)
400
500
Figure 11. POWER SPECTRUM DENSITY OF THE TANGENTIAL AND
NORMAL FORCES.
of oscillations of fingers of a manipulators. Since those fingers
did not have sweat glands, their results are not comparable with
the results reported here.
EXPERIMENTAL RESULTS IN VIRTUAL ENVIRONMENTS
We have so far implemented the stick-slip model on a flat
virtual surface and asked users to touch it by the Sarcos Dextrous
DISCUSSION
This paper has presented a friction model for virtual environments based on characteristics of human finger pads. The
frictional behavior of the human finger pad is a complex phenomenon which cannot be emulated accurately in virtual environment. However, our experiments showed that we can “reasonably” approximate finger pad behavior for implementation in
a virtual environment.
We assumed that friction is proportional to the normal force
in stick phase. Although there is some approximation in this assumption, we believe it is an acceptable assumption for virtual
environments. Another source of error is hysteresis which is
more significant for some subjects than results show in Figure
8. Also, a third order spring is more appropriate for some subjects than a linear spring in stick phase. Since it is not practical to
determine the appropriate spring for any individual subject a pri-
ori, it is argued that a linear spring can be applied for all subjects
[13].
ACKNOWLEDGMENT
This research was supported by NSF Grant MIP-9420352
and by NSERC NCE IRIS Project AMD-2.
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